CeCd$_3$As$_3$ is a rare-earth triangular-lattice antiferromagnet with large inter-layer separation. Our field-dependent heat capacity measurements at dilution fridge temperatures allow us to trace the field-evolution of spin-excitation gaps throughout antiferromagnetic and paramagnetic regions. The distinct gap evolution places strong constraints on microscopic pseudo-spin model, which, in ret...

We introduce a “Coulombian renormalized energy” W which is a logarithmic type of interaction between points in the plane, computed by a “renormalization.” We prove various of its properties, such as the existence of minimizers, and show in particular, using results from number theory, that among lattice configurations the triangular lattice is the unique minimizer. Its minimization in general r...

Honeycombs with thermal expansion coefficients equal to zero are described analytically. The two dimensional lattice microstructure designs described are made of positive expansion materials. This work builds upon previous results, and provides further analysis into creating an optimal rib cross section. The design of ribs with Tee shaped and I shaped cross sections is developed. The behavior o...

We study the energetics of vortices and vortex lattices produced by rotation in the cyclic phase of F=2 spinor condensates. In addition to the familiar triangular lattice predicted by Tkachenko for 4He, many more complex lattices appear in this system as a result of the spin degree of freedom. In particular, we predict a magnetic-field-driven transition from a triangular lattice to a honeycomb ...

We study the folding of the regular two-dimensional triangular lattice embedded in the regular three-dimensional Face-Centred Cubic lattice, a discrete model for the crumpling of membranes. Possible folds are complete planar folds, folds with the angle of a regular tetrahedron (71 •) or with that of a regular octahedron (109 •). We study this model in the presence of a negative bending rigidity...

Mechanical instability takes different forms in various ordered and disordered systems and little is known about how thermal fluctuations affect different classes of mechanical instabilities. We develop an analytic theory involving renormalization of rigidity and coherent potential approximation that can be used to understand finite-temperature mechanical stabilities in various disordered syste...

We prove that the q-state Potts antiferromagnet on a lattice of maximum coordination number r exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) whenever q > 2r. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay for q 7), triangular lattice (q 11), hexagonal lattice (q 4), and Kagom e l...

We prove that the q-state Potts antiferromagnet on a lattice of maximum coordination number r exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) whenever q > 2r. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay for q ≥ 7), triangular lattice (q ≥ 11), hexagonal lattice (q ≥ 4), and Kag...